SELF-REFERENTIAL THEORIES

Abstract We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axi...

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Published inThe Journal of symbolic logic Vol. 85; no. 4; pp. 1687 - 1716
Main Author ALEXANDER, SAMUEL A.
Format Journal Article
LanguageEnglish
Published Pasadena Cambridge University Press 01.12.2020
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Summary:Abstract We study the structure of families of theories in the language of arithmetic extended to allow these families to refer to one another and to themselves. If a theory contains schemata expressing its own truth and expressing a specific Turing index for itself, and contains some other mild axioms, then that theory is untrue. We exhibit some families of true self-referential theories that barely avoid this forbidden pattern.
ISSN:0022-4812
1943-5886
1943-5886
DOI:10.1017/jsl.2020.54